Aseries lrc circuit consists of a 12.0-mh inductor, a 15.0-µf capacitor, a resistor, and a 110-v (rms) ac voltage source. if the impedance of this circuit is 45.0 ω at resonance, what is its impedance at a frequency twice the resonance frequency?

61.85 ohm

Explanation:

L = 12 m H = 12 x 10^-3 H, C = 15 x 10^-6 F, Vrms = 110 V, R = 45 ohm

Let ω0 be the resonant frequency.

ω0 = 2357 rad/s

ω = 2 x 2357 = 4714 rad/s

XL = ω L = 4714 x 12 x 10^-3 = 56.57 ohm

Xc = 1 / ω C = 1 / (4714 x 15 x 10^-6) = 14.14 ohm

Impedance, Z =

Z = \sqrt{45^{2}+\left ( 56.57-14.14 )^{2}} = 61.85 ohm

Thus, the impedance at double the resonant frequency is 61.85 ohm.

wavelength divides in half and speed stays the same.